Question

The number of common terms in the two sequences: 15, 19, 23, 27, . . . . , 415 and 14, 19, 24, 29, . . . , 464 is

• A. 18
• B. 19
• C. 21
• D. 20

Answer 1

Answer: (D)

20

Answer 2

Both sequences are in arithmetic progression.
The common difference $(d_1​)$ for the first sequence is 4.
The common difference $(d_2​)$ for the second sequence is 5.
The first common term is 19.
The common terms will also form an arithmetic progression with a common difference
$LCM(d1​,d2​)=LCM(4,5)=20.$

Let there be $‘n’$ terms in this sequence; then, the last term would be less than or equal to 415.

i.e. $a+(n−1)d≤415$
$19+(n−1)×20≤415$
$(n−1)×20≤415−19$
$(n−1)×20≤396$
$(n−1)=[\frac{396}{20}​]$ where [ ] is the greatest integer
$(n−1)=19,$
so $n=20$